Archive for March, 2009
We struggled to see the exact import of this paper. Cian worried that ‘ontological commitment’ was a philosophical technical term, and that even a really good account of it would still not tell us too much about what really exists. Perhaps the motivation is that Rayo wants to emphasize that the characterization of ontological commitment can be kept apart from Quine’s criterion. Quine’s criterion (to be is to be the value of a variable) has perhaps come to seem constitutive of ontological commitment for some philosophers, which leaves no room for non-Quinean accounts of the ontology of (say) mathematics.
I wondered about an attempt at explaining demand-talk in terms of necessitation. The obvious account, that the truth of P demands that the world contains F iff necessarily(p → Fs exist), ends up saying that asserting any true proposition commits us to the existence of all necessary existents. So we can try ruling necessary existents out by fiat. Say that the truth of p demands of the world that it contain Fs . Maybe this is equivalent to saying that a) necessarily(p → Fs exist) and b) not necessarily p. The problem with that (supposing numbers are necessary existents), it would come out false that the truth of <there are numbers> demands of the world that it contain numbers, and hence that asserting ‘there are numbers’ commits you to numbers. Indeed, it would never be the case that asserting the existence of necessary existents commits you to those necessary existents. I’m not sure what Rayo would think about this. On the one hand, he does want to say that true propositions of mathematics have trivial truth-conditions and hence we can assert them without being committed to numbers. On the other hand, this account of demand-talk would beg the question in favour of the falsity of Quine’s criterion (at least a version of the criterion which is generalized to the language of mathematics) and Rayo seems to be unwilling to build either the truth or falsity of Quine’s criterion into the notion of ontological commitment. So I guess if we want to remain neutral on Quine’s criterion (at least as far as characterising the notion of ontological commitment is concerned) then demand-talk is going to have to remain primitive and unanalysed. But if we take a nominalist line which rejects Quine’s criterion, then we can potentially give a straightforward account of ontological commitment in terms of necessitation.
Rayo suggests that the ‘demands of the world that it contain Fs’ should be generalized to ‘demands of the totality of everything there is that it contain Fs’ if you are a modal realist. If so, I don’t see why we shouldn’t use this latter formulation in general, since we don’t want an account of ontological commitment to beg any questions about modal ontology.
We thought that the ‘extrinsic property worry’ for Quine’s criterion was badly characterised by the extrinsic/intrinsic distinction. Not only, as Rayo admits, do not all extrinsic properties cause trouble, but some intrinsic properties like ‘is composite’ also cause trouble. Plausibly, a thing being composite demands of the world that the world contain parts, but ‘for some x, x is composite’ doesn’t need to have parts among the values of its variables.
Summary – White makes a fairly compelling attack on ‘mushy credence views’ with the simple but ingenious example of the coin which has been painted p on one side, and not-p on the other, with whichever is correct going on the ‘heads’ side. If your credence in p starts out mushy, mushy credence views seem to predict either that your credence in ‘heads came up’ should go mushy, or that your credence in p should go precise. But either option seems to conflict with some fairly obvious premises. I was convinced by this side of the argument – and it does give us good reason to go back to the principle of indifference and see what was wrong with it.
We wondered whether the coin argument would work for unknowable p – as White states the argument, it relies on the person running the coin toss knowing whether p. But it seems we could replace ‘knows whether p” in the example with ‘has credence 1 either in p or in not-p”, and the same sort of objection recurs for the mushy credence view.
The problems for the mushy credence responses take us back to the multiple partitions problem, and to cases like van Fraassen’s cube factory. Given that a mystery cube is less than 2 feet wide, what should our credence be that it’s less than 1 foot wide? The answer given by the principle of indifference depends on whether we partition its state space by surface area, by volume, or by side length.
White says he ‘doesn’t really have an answer’ as to what to say about cases like this. But an answer can be extracted from what he says next, and I think it’s a plausible one. This is that our evidence does in fact tell on the question of which partition to use (or which weighted combination of partitions, perhaps) – it’s just that we’re not generally in a position to know what partition our evidence supports. This seems a good response to me, and also a promising direction for further enquiry. Principles governing rational choice of state-space partition for simple chance set-ups seem like viable topics of study – it seems at least plausible that we incorporate some such principles into folk theory, even if we don’t know precisely which ones they are.
The obvious question to ask in this connection is ‘what determines appropriateness for a choice of state space’? Different answers to this question look like giving different strengths of normativity for the rationality of applying them. For example, assume an indeterministic world – the ideal choice of state-space partition for some system’s state-space consists in a measure given by the laws over the state space given by the laws and the whole past history. But the norm ‘match credences to probabilities given by this ideal partition’ is very demanding to satisfy. To do it, we’d have to at least know the true laws and the whole past history, and be able to do the number-crunching. No existing rational being can get close. Compare this with norm ‘believe only the truth’ for rational belief in general.
A less demanding norm would say that the rational choice for state-space partition is the one based on the measure given by the laws over the state-space given by the laws and our evidence about the past history. That’s a lot less restrictive, so the state-space would be a lot larger. This seems to correspond better to our epistemic state. But it’s still absurdly demanding – we can weaker the norm further, and say that the rational choice for state-space partition is the one given by current best scientific theory over the state-space given by current best scientific theory and our evidence about the past history.
This final norm – appealing to evidence about the past plus current best scientific theory – seems to me like an appropriate candidate for the rational norm governing state-space partition choices in applications of the principle of indifference. It still, in a sense, requires logical omniscience to know what exactly is rational according to it – because we don’t in general know how the factors determining the partition determine it in detail. That requires accurate modelling of the system in question. But we can say something basic about which factors have an influence.
One thing that stood out for me is that White uses a non-Lewisian notion of objective chance throughout. For him chances seem to be (roughly) probabilities conditionalized on our actual evidence, where our priors are the ones a rational agent who knew the laws of nature would have. This means that the chance of a coin already tossed but not revealed can be 1/2 – Lewisian chances, which are conditionalized on the whole history, don’t allow for this. So White may have been thinking of one of the less demanding norms, perhaps the second of the three mentioned above.